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Mathematics

D-Index
62
Citations
16853
World Ranking
472
National Ranking
23

Research.com Recognitions

  • 2017 - SIAM Fellow For contributions to numerical methods for optimal control and model reduction.

Overview

Peter Benner is affiliated with the Max Planck Institute for Dynamics of Complex Technical Systems in Germany. Their research primarily spans the fields of engineering and physics and astronomy, with significant contributions to statistical and nonlinear physics, control and systems engineering, numerical analysis, computational mechanics, and computational theory and mathematics.

The scientist's work covers major topics such as model reduction and neural networks, numerical methods for differential equations, probabilistic and robust engineering design, matrix theory and algorithms, control systems and identification, real-time simulation and control systems, and fluid dynamics and vibration analysis.

Peter Benner has published research in several frequent venues, including:

  • arXiv (Cornell University)
  • PAMM
  • Advances in Computational Mathematics
  • Zenodo (CERN European Organization for Nuclear Research)
  • Computer Methods in Applied Mechanics and Engineering

Their recent papers include:

  • Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms, 2020, Computer Methods in Applied Mechanics and Engineering
  • An artificial neural network for surrogate modeling of stress fields in viscoplastic polycrystalline materials, 2023, npj Computational Materials
  • Discovery of nonlinear dynamical systems using a Runge-Kutta inspired dictionary-based sparse regression approach, 2022, Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences
  • Interpolation-Based Model Order Reduction for Polynomial Systems, 2021, SIAM Journal on Scientific Computing
  • Frequency- and time-limited balanced truncation for large-scale second-order systems, 2020, Linear Algebra and its Applications

Frequent coauthors collaborating with Peter Benner include:

  • Pawan Goyal
  • Igor Pontes Duff
  • Lihong Feng
  • Jan Heiland
  • Steffen W. R. Werner

Additionally, Peter Benner has contributed to book publications. They have authored works published by Springer Nature, including Model Reduction of Complex Dynamical Systems (2021), and Springer Studium Mathematik - Master with Modellreduktion (2024).

In recognition of their contributions, Peter Benner was named a SIAM Fellow in 2017 for work related to numerical methods for optimal control and model reduction.

Best Publications

  • A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

    Peter Benner;Serkan Gugercin;Karen Willcox

  • Dimension Reduction of Large-Scale Systems

    Peter Benner;Peter Benner;Volker Mehrmann;Sorensen Danny C.

  • Numerical solution of large‐scale Lyapunov equations, Riccati equations, and linear‐quadratic optimal control problems

    Peter Benner;Jing-Rebecca Li;Thilo Penzl

  • Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective

    Ulrike Baur;Peter Benner;Lihong Feng

  • SLICOT—A Subroutine Library in Systems and Control Theory

    Peter Benner;Peter Benner;Volker Mehrmann;Vasile Sima;Sabine Van Huffel

  • Model Reduction and Approximation: Theory and Algorithms

    Peter Benner;Albert Cohen;Mario Ohlberger;Karen Willcox

  • Lyapunov Equations, Energy Functionals, and Model Order Reduction of Bilinear and Stochastic Systems

    Peter Benner;Tobias Damm

  • Interpolatory Projection Methods for Parameterized Model Reduction

    Ulrike Baur;Christopher Beattie;Peter Benner;Serkan Gugercin

  • On the ADI method for Sylvester equations

    Peter Benner;Ren-Cang Li;Ninoslav Truhar

  • Solving stable generalized Lyapunov equations with the matrix sign function

    Peter Benner;Peter Benner;Enrique S. Quintana-Ortí

  • Solving large-scale control problems

    P. Benner

  • Numerical Solution of Large and Sparse Continuous Time Algebraic Matrix Riccati and Lyapunov Equations: A State of the Art Survey

    Peter Benner;Jens Saak

  • Interpolation-Based H2-Model Reduction of Bilinear Control Systems

    Peter Benner;Peter Benner;Tobias Breiten

  • A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencils

    Peter Benner;Peter Benner;Volker Mehrmann;Hongguo Xu

  • An exact line search method for solving generalized continuous-time algebraic Riccati equations

    P. Benner;R. Byers

  • Two-Sided Projection Methods for Nonlinear Model Order Reduction

    Peter Benner;Tobias Breiten

  • Numerical Computation of Deflating Subspaces of Skew-Hamiltonian/Hamiltonian Pencils

    Peter Benner;Peter Benner;Ralph Byers;Volker Mehrmann;Hongguo Xu

  • An Implicitly Restarted Symplectic Lanczos Method for the Hamiltonian Eigenvalue Problem

    Peter Benner;Heike Faβbender

  • Low rank methods for a class of generalized Lyapunov equations and related issues

    Peter Benner;Tobias Breiten

  • Model Reduction of Parametrized Systems

    Peter Benner;Mario Ohlberger;Anthony T. Patera;Gianluigi Rozza

  • A new method for computing the stable invariant subspace of a real Hamiltonian matrix

    Peter Benner;Volker Mehrmann;Hongguo Xu

Frequent Co-Authors

Enrique S. Quintana-Ortí
Enrique S. Quintana-Ortí Universitat Politècnica de València
Volker Mehrmann
Volker Mehrmann Technical University of Berlin
Ralph Byers
Ralph Byers University of Kansas
Andreas Seidel-Morgenstern
Andreas Seidel-Morgenstern Max Planck Society
Kai Sundmacher
Kai Sundmacher Max Planck Institute for Dynamics of Complex Technical Systems
Daniel Kressner
Daniel Kressner École Polytechnique Fédérale de Lausanne
Athanasios C. Antoulas
Athanasios C. Antoulas Rice University
Serkan Gugercin
Serkan Gugercin Virginia Tech
Karen Willcox
Karen Willcox The University of Texas at Austin
Mario Ohlberger
Mario Ohlberger University of Münster

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